The problem of computing the minimum tiling path (MTP) from a set of clones arranged in a physical map is a cornerstone of hierarchical (clone-by-clone) genome sequencing projects. We formulate this problem in a graph theoretical framework, and then solve by a combination of minimum hitting set and minimum spanning tree algorithms. The tool implementing this strategy, called FMTP, shows improved performance compared to the widely used software FPC. When we execute FMTP and FPC on the same physical map, the MTP produced by FMTP covers a higher portion of the genome, and uses a smaller number of clones. For instance, on the rice genome the MTP produced by our tool would reduce by about 11 percent the cost of a clone-by-clone sequencing project. Source code, benchmark data sets, and documentation of FMTP are freely available at http://code.google.com/p/fingerprint-basedminimal-tiling-path/ under MIT license.